a two digit number is 6 more than 4 times the sum of its digit. if 27 is added to the number its digits are reversed. find the number
Answers
Step-by-step explanation:
then answer is. 58 because let us take first condition as equation 1 and 2nd condition as equation 2 then by simplifying we get answe
Solution :
Let us assume that the number here is xy .
According to the first condition :
This number is 6 more than 4 times the sum of its digits .
> xy = 6 + 4(x+y)
> 10x + y = 6 + 4x + 4y
> 6x = 6 + 3y
> 2x = 2 + y .
> y = 2x - 2
This is an important result to be used in the following condition .
xy + 27 = yx
> 10x + y + 27 = 10y + x
> 9x + 27 = 9y
> x + 3 = y
But, y = 2x -2
Hence,
2x - 2= x + 3
> x = 5
> y = 8.
Thus , the required number becomes 58.
This is the answer,
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